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A particle starts from rest and moves with acceleration \( a \) which varies with time \( t \) as \( a=k t \) where \( k \) is a constant. The displacement \( s \) of the particle at time \( t \) is
(A) \( \frac{1}{2} k t^{2} \)
(B) \( \frac{1}{2} a t^{2} \)
(C) \( \frac{1}{6} a t^{2} \)
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